Minimum Basis setsA minimum basis set is one in which a single basis function is used for each orbital in a on the atom. However, for atoms such as lithium, basis functions of p type are added to the basis functions corresponding to the 1s and 2s orbitals of each atom. For example, each atom in the first row of the periodic system (Li - Ne) would have a basis set of five functions (two s functions and three p functions).In a minimum basis set, a single basis function is used for each atomic orbital on each constituent atom in the system.The most common minimal basis set is STO-nG, where n is an integer. This (n) value represents the number GTOs used to approximate the Slater Type orbital (STO) for both core and valence orbitals. Minimal basis sets typically give rough results that are insufficient for research-quality publication, but are much cheaper (less calculations requires) than the larger basis sets discussed below. Commonly used minimal basis sets of this type are: STO-3G, STO-4G, and STO-6G.
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Open the Gaussian Calculations Setup window from the main window's Calculate menu. The following choices will set up a triplet-state geometry optimization using density functional theory and the 6-31g(d) basis set. Augmented Gaussian basis sets of double and triple zeta valence qualities plus polarization functions for the atoms K and from Sc to Kr are presented.
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A basis set in and is a set of (called basis functions) that is used to represent the electronic wave function in the or in order to turn the partial differential equations of the model into algebraic equations suitable for efficient implementation on a computer.The use of basis sets is equivalent to the use of an approximate resolution of the identity. The single-particle states are then expressed as linear combinations of the basis functions.The basis set can either be composed of (yielding the approach), which is the usual choice within the quantum chemistry community, or which are typically used within the solid state community. Several types of atomic orbitals can be used:, or numerical atomic orbitals. Out of the three, Gaussian-type orbitals are by far the most often used, as they allow efficient implementations of methods. Contents.Introduction In modern, calculations are performed using a finite set of. When the finite basis is expanded towards an (infinite) complete set of functions, calculations using such a basis set are said to approach the complete basis set (CBS) limit.
In this article, basis function and atomic orbital are sometimes used interchangeably, although the basis functions are usually not true atomic orbitals, because many basis functions are used to describe polarization effects in molecules.Within the basis set, the is represented as a, the components of which correspond to coefficients of the basis functions in the linear expansion. In such a basis, one-electron correspond to (a.k.a. Rank two ), whereas two-electron operators are rank four tensors.When molecular calculations are performed, it is common to use a basis composed of, centered at each nucleus within the molecule ( ).
The physically best motivated basis set are (STOs),which are solutions to the of, and decay exponentially far away from the nucleus. It can be shown that the of and also exhibit exponential decay. Furthermore, S-type STOs also satisfy at the nucleus, meaning that they are able to accurately describe electron density near the nucleus. However, hydrogen-like atoms lack many-electron interactions, thus the orbitals do not accurately describe.Unfortunately, calculating integrals with STOs is computationally difficult and it was later realized by that STOs could be approximated as linear combinations of (GTOs) instead. Because the product of two GTOs can be written as a linear combination of GTOs, integrals with Gaussian basis functions can be written in closed form, which leads to huge computational savings (see ).Dozens of Gaussian-type orbital basis sets have been published in the literature.
Basis sets typically come in hierarchies of increasing size, giving a controlled way to obtain more accurate solutions, however at a higher cost.The smallest basis sets are called minimal basis sets. A minimal basis set is one in which, on each atom in the molecule, a single basis function is used for each orbital in a calculation on the free atom. For atoms such as lithium, basis functions of p type are also added to the basis functions that correspond to the 1s and 2s orbitals of the free atom, because lithium also has a 1s2p bound state.
For example, each atom in the second period of the periodic system (Li - Ne) would have a basis set of five functions (two s functions and three p functions). A d-polarization function added to a p orbitalThe minimal basis set is close to exact for the gas-phase atom. In the next level, additional functions are added to describe polarization of the electron density of the atom in molecules. These are called polarization functions. For example, while the minimal basis set for hydrogen is one function approximating the 1s atomic orbital, a simple polarized basis set typically has two s- and one p-function (which consists of three basis functions: px, py and pz). This adds flexibility to the basis set, effectively allowing molecular orbitals involving the hydrogen atom to be more asymmetric about the hydrogen nucleus. This is very important for modeling chemical bonding, because the bonds are often polarized.
Similarly, d-type functions can be added to a basis set with valence p orbitals, and f-functions to a basis set with d-type orbitals, and so on.Another common addition to basis sets is the addition of diffuse functions. These are extended Gaussian basis functions with a small exponent, which give flexibility to the 'tail' portion of the atomic orbitals, far away from the nucleus. Diffuse basis functions are important for describing anions or dipole moments, but they can also be important for accurate modeling of intra- and intermolecular bonding.Minimal basis sets The most common minimal basis set is, where n is an integer. This n value represents the number of Gaussian primitive functions comprising a single basis function. In these basis sets, the same number of Gaussian primitives comprise core and valence orbitals. Minimal basis sets typically give rough results that are insufficient for research-quality publication, but are much cheaper than their larger counterparts.
Commonly used minimal basis sets of this type are:. STO-3G. STO-4G.
STO-6G. STO-3G. Polarized version of STO-3GThere are several other minimum basis sets that have been used such as the MidiX basis sets.Split-valence basis sets During most molecular bonding, it is the valence electrons which principally take part in the bonding. In recognition of this fact, it is common to represent valence orbitals by more than one basis function (each of which can in turn be composed of a fixed linear combination of primitive Gaussian functions). Basis sets in which there are multiple basis functions corresponding to each valence atomic orbital are called valence double, triple, quadruple-zeta, and so on, basis sets (zeta, ζ, was commonly used to represent the exponent of an STO basis function ). Since the different orbitals of the split have different spatial extents, the combination allows the electron density to adjust its spatial extent appropriate to the particular molecular environment.
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In contrast, minimal basis sets lack the flexibility to adjust to different molecular environments.Pople basis sets The notation for the split-valence basis sets arising from the group of is typically X-YZg. In this case, X represents the number of primitive Gaussians comprising each core atomic orbital basis function. The Y and Z indicate that the valence orbitals are composed of two basis functions each, the first one composed of a linear combination of Y primitive Gaussian functions, the other composed of a linear combination of Z primitive Gaussian functions. In this case, the presence of two numbers after the hyphens implies that this basis set is a split-valence double-zeta basis set. Split-valence triple- and quadruple-zeta basis sets are also used, denoted as X-YZWg, X-YZWVg, etc. Jensen, Frank (2013). 'Atomic orbital basis sets'.
WIREs Comput. 3 (3): 273–295. Errol G. Lewars (2003-01-01). Computational Chemistry: Introduction to the Theory and Applications of Molecular and Quantum Mechanics (1st ed.).
Springer.; Feller, David (1986). 'Basis set selection for molecular calculations'. 86 (4): 681–696. Ditchfield, R; Hehre, W.J; Pople, J. 'Self-Consistent Molecular-Orbital Methods. An Extended Gaussian-Type Basis for Molecular-Orbital Studies of Organic Molecules'. 54 (2): 724–728.
Moran, Damian; Simmonett, Andrew C.; Leach, Franklin E. III; Allen, Wesley D.; Schleyer, Paul v. R.; Schaefer, Henry F. 'Popular theoretical methods predict benzene and arenes to be nonplanar'. 128 (29): 9342–9343. Dunning, Thomas H.
'Gaussian basis sets for use in correlated molecular calculations. The atoms boron through neon and hydrogen'. 90 (2): 1007–1023. Jensen, Frank (2001). 'Polarization consistent basis sets: Principles'.
115 (20): 9113–9125. Manninen, Pekka; Vaara, Juha (2006). 'Systematic Gaussian basis-set limit using completeness-optimized primitive sets. A case for magnetic properties'. 27 (4): 434–445. Chong, Delano P. 'Completeness profiles of one-electron basis sets'.
73 (1): 79–83. Lehtola, Susi (2015). 'Automatic algorithms for completeness-optimization of Gaussian basis sets'. 36 (5): 335–347.All the many basis sets discussed here along with others are discussed in the references below which themselves give references to the original journal articles:.
Levine, Ira N. Quantum Chemistry. Englewood Cliffs, New jersey: Prentice Hall. Pp. 461–466. Cramer, Christopher J.
Essentials of Computational Chemistry. Chichester: John Wiley & Sons, Ltd. Pp. 154–168. Jensen, Frank (1999). Introduction to Computational Chemistry.
John Wiley and Sons. Pp. 150–176. Leach, Andrew R. Molecular Modelling: Principles and Applications. Singapore: Longman. Pp. 68–77. Hehre, Warren J.
A Guide to Molecular Mechanics and Quantum Chemical Calculations. Irvine, California: Wavefunction, Inc. Pp. 40–47. Moran, Damian; Simmonett, Andrew C.; Leach, Franklin E.; Allen, Wesley D.; Schleyer, Paul v.
R.; Schaefer, Henry F. 'Popular Theoretical Methods Predict Benzene and Arenes To Be Nonplanar'. Journal of the American Chemical Society. 128 (29): 9342–3. Choi, Sunghwan; Kwangwoo, Hong; Jaewook, Kim; Woo Youn, Kim (2015). 'Accuracy of Lagrange-sinc functions as a basis set for electronic structure calculations of atoms and molecules'.
The Journal of Chemical Physics. 142 (9): 094116.External links.